Question 1197028
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       x +     y +     z = 10000    (1)

    0.1x + 0.12y + 0.15z =  1310    (2)

   -0.1x - 0.12y + 0.15z =   190    (3)


Add equations (2) and (3).  You will get

                   0.3z = 1310 + 190 = 1500,   hence  z = 1500/0.3 = 5000.


Substitute z= 5000 into equations (1) and (2).   You will get

       x +     y = 5000    (4)

    0.1x + 0.12y =  560    (5)


Multiply equation (5) by 10; keep equation (4) as is.  You will get then

       x +     y = 5000    (4')

       x +  1.2y = 5600    (5')


Subtract (4') from (5').  You will get

            0.2y =  600;  hence  y = 600/0.2 = 3000.


Now use equation (1) to find x.  Substitute  y= 3000  and  z= 5000 into (1)

    x + 3000 + 5000 = 10000.


It gives  x = 10000 - 3000 - 5000 = 2000.


<U>ANSWER</U>.  $2000 invested at 10%;  $3000 invested at 12%  and  $5000 invested at 15%.


<U>CHECK</U>.   Please check it on your own, substituting the values into equations (2) and (3).
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Solved.